This probably has to do with the path to the image in relation to the target page that the content has been applied to.
On the page that you cannot view the image from what is listed in the source code for the image's location? This is the first thing to check, if the path is just a little off here you can account for that during your content insert or update. When you are adding things to your editor it is best to think about the paths from the location where the content will be coming from in the end.
For example, if you have your HTML Editor on a page that is in a sub director on your site and you and the image to the editor so that you can see it the path might look like this:
If you end up putting this content on your index page in the root of the site the link to the image might still be like it is above. The problem is that on your index page this is not the correct path to the image, the correct path to this image from your home page would look like this: